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arXiv · 2310.11419

A note on an effective bound for the gonality conjecture

Alexander Duncan·Wenbo Niu·Jinhyung Park
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Abstract

The gonality conjecture, proved by Ein--Lazarsfeld, asserts that the gonality of a nonsingular projective curve of genus $g$ can be detected from its syzygies in the embedding given by a line bundle of sufficiently large degree. An effective result obtained by Rathmann says that any line bundle of degree at least 4g-3 would work in the gonality theorem. In this note, we improve the degree bound to 4g-4 with two exceptional cases.

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Alexander Duncan, Wenbo Niu, Jinhyung Park. 2023-10-17. A note on an effective bound for the gonality conjecture. https://arxiv.org/abs/2310.11419

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